Let , where denotes the greatest integer less than or equal to . Determine all real…

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

f(x)=|x|+\lfloor x\rfloor

, where

\lfloor x\rfloor

denotes the greatest integer less than or equal to

x

. Determine all real numbers at which

f

is not differentiable.